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Generalization of Queueing Network Product Form Solutions to Stochastic Petri Nets
February 1991 (vol. 17 no. 2)
pp. 99-107

A new solution is given for the steady-state probability computation of closed synchronized queuing networks. A closed synchronized queuing network is a particular Markov stochastic Petri net (a bounded and monovaluated Petri net with a strongly connected reachability graph and constant firing rates independent of markings). It is shown that the steady-state probability distribution can be expressed using matrix products. The results generalize the Gordon-Newell theorem. The solution is similar to the Gordon-Newell product form using matrix and vectors instead of scalars. A prototype solver developed from this result is presented.

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Index Terms:
performance evaluation; queueing network product form solutions; stochastic Petri nets; steady-state probability; closed synchronized queuing networks; Markov stochastic Petri net; strongly connected reachability graph; constant firing rates; matrix products; Gordon-Newell theorem; performance evaluation; Petri nets; queueing theory
G. Florin, S. Natkin, "Generalization of Queueing Network Product Form Solutions to Stochastic Petri Nets," IEEE Transactions on Software Engineering, vol. 17, no. 2, pp. 99-107, Feb. 1991, doi:10.1109/32.67591
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